New high-resolution visible emission spectra of the MgH molecule have been recorded with high signal-to-noise ratios using a Fourier transform spectrometer. Many bands of the A (II)-I-2 -> X (2)Sigma(+) and B' (2)Sigma(+) -> X (2)Sigma(+) electronic transitions of (MgH)-Mg-24 were analyzed; the new data span the v' = 0-3 levels of the A (II)-I-2 and B'(2)Sigma(+) excited states and the v '' = 0-11 levels of the X (2)Sigma(+) ground electronic state. The vibration-rotation energy levels of the perturbed A (II)-I-2 and B' (2)Sigma(+) states were fitted as individual term values, while those of the X (2)Sigma(+) ground state were fitted using the direct-potential-fit approach. A new analytic potential energy function that imposes the theoretically correct attractive potential at long-range, and a radial Hamiltonian that includes the spin-rotation interaction were employed, and a significantly improved value for the ground state dissociation energy of MgH was obtained. The v '' = 11 level of the X (2)Sigma(+) ground electronic state was found to be the highest bound vibrational level of 24 MgH, lying only about 13 cm(-1) below the dissociation asymptote. The equilibrium dissociation energy for the X (2)Sigma(+) ground state of (MgH)-Mg-24 has been determined to, be D-e = 11104.7 +/- 0.5 cm(-1) (1.37681 +/- 0.00006 eV), whereas the zero-point energy (v '' = 0) is 739.11 +/- 0.01 cm(-1). The zero-point dissociation energy is therefore D-0 = 10365.6 +/- 0.5 cm(-1) (1.28517 +/- 0.00006 eV). The uncertainty in the new experimental dissociation energy of MgH is more than 2 orders of magnitude smaller than that for the best value available in the literature. MgH is now the only hydride molecule other than H-2 itself for which all bound vibrational levels of the ground electronic state are observed experimentally and for which the dissociation energy is determined with subwavenumber accuracy.